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Solar PhysicsDOI: 10.1007/•••••-•••-•••-••••-•

Evolution and Flare Activity of δ-Sunspots in Cycle

23

K. Takizawa1 · R. Kitai1,2

c© Springer ••••

Abstract The emergence and magnetic evolution of solar active regions (ARs)of βγδ-type, which are known to be highly flare-productive, were studied withthe SOHO/MDI data in Cycle 23. We selected 31 ARs that can be observedfrom their birth phase, as unbiased samples for our study. From the analysis ofthe magnetic topology (twist and writhe), we obtained the following results. i)Emerging βγδ ARs can be classified into three topological types as “quasi-β”,“writhed” and “top-to-top”. ii) Among them, the “writhed” and “top-to-top”types tend to show high flare activity. iii) As the signs of twist and writhe agreewith each other in most cases of the “writhed” type (12 cases out of 13), wepropose a magnetic model in which the emerging flux regions in a βγδ ARare not separated but united as a single structure below the solar surface. iv)Almost all the “writhed”-type ARs have downward knotted structures in themid portion of the magnetic flux tube. This, we believe, is the essential propertyof βγδ ARs. v) The flare activity of βγδ ARs is highly correlated not only withthe sunspot area but also with the magnetic complexity. vi) We suggest thatthere is a possible scaling-law between the flare index and the maximum umbralarea.

Keywords: Active regions · Magnetic fields · Photosphere

1. Introduction

A sunspot group with umbrae of opposite polarity within a single commonpenumbra is called the δ-sunspot group (Kunzel, 1960). It is well known that ma-jor flares almost always occur in δ-sunspot groups (Tanaka, 1975; Zirin and Liggett,1987; Sammis et al., 2000). Hence, investigation of the formation and evolutionof the δ-configuration is the key in understanding the major flare activities.

Zirin and Liggett (1987) classified the formation of δ-spots in three typesas follows: i) Emergence of a single complex active region (AR) formed below

1 Kwasan and Hida Observatories, Kyoto University,Yamashina-ku, Kyoto 607-8417, Japan2 Bukkyo University, Kita-ku, Kyoto 603-8301, Japanemail: takizawa@kwasan.kyoto-u.ac.jpemail: kitai@kwasan.kyoto-u.ac.jp

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Takizawa and Kitai

the surface, i.e., the so-called “island δ-spot”, ii) emergence of large satellite

spots near a larger and older sunspot, and iii) collision of sunspots of opposite

polarity from different dipoles. Then Ikhsanov et al. (2004), from their morpho-

logical study of δ-spots, classified the magnetic topology of collisional interaction

between two major emerging flux tubes into three types, namely “vertical (top-

by-top) collision”, “lateral (side-by-side) collision”, and “frontal (foot-by-foot)

collision” (see also Ikhsanov and Marushin, 2003). Although these researches

show a variety of ways of δ-spot formation, they did not give us a detailed

physical view of the formation of δ-spots. This is because their classifications

were phenomenological.

Succeeding researches (Kurokawa, 1987; Tanaka, 1991; Leka et al., 1996; van Driel-Gesztelyi et al.,

1997; Ishii et al., 1998; Linton et al., 1999; Fan et al., 1999; Lopez Fuentes et al.,

2000) have found several physical characteristics of active δ-spots, in that they

have strong magnetic shear structures in their magnetic neutral line area and

their opposite polarities rotate around each other. These characteristics were

interpreted as due to the emergence of a kinked flux rope. Ishii et al. (1998) and

Kurokawa et al. (2002) proposed that the δ-spot is produced by the emergence

of a twisted magnetic flux rope whose strong shear produces high flare activities.

Poisson et al. (2013) suggested that the δ-spot could be due to the emergence of

a deformed single tube which has a downward convex structure at its middle part

with kinking. Thus the twist and writhe of a magnetic rope is now considered

as a key factor for the development of δ-spots and the associated flare activities

which sometime show sigmoidal morphology (Rust and Kumar, 1996).

Although a number of case studies revealed the important characteristics of

δ-spot evolution, we have not yet had a conclusive observational and physical

view of the δ-spot formation. In this article, we tried to obtain more clues on

this issue by surveying the δ-spots in solar activity cycle 23 paying attention

to magnetic helicity (twist and writhe). Among all the δ-spots in Cycle 23, we

selected those which can be studied from their birth on the visible solar disk

in order to unambiguously study the magnetic connection between component

sunspots in a group. Further we limited the samples to the βγδ regions, as

they show the highest flare activity (Sammis et al., 2000). The magnetograms

and the continuum images taken with the Michelson Doppler Imager (MDI;

Scherrer et al., 1995) on board the Solar and Heliospheric Observatory (SOHO;

Domingo et al., 1995) were used to follow the evolution of the ARs.

Our study shows that the flare-active δ-spots are mainly formed by the emer-

gence of writhed and twisted magnetic tubes, which appear as a quadrupolar

magnetic configuration on the photosphere. Even the appearance of a more

complex δ-configuration can be interpreted as a modification to this basic con-

figuration. On the other hand, the flare activity is low when the magnetic tubes

in the δ-configuration show insignificant writhe or twist.

In Section 2, we describe the data used in our study and the analysis method.

In Section 3, we present our detailed analysis on some representative cases and

summarize our statistical analysis. Finally, we give discussion on our results and

our conclusions in Sections 4 and 5, respectively.

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Evolution and Flare Activity of δ-Spots in Cycle 23

2. Data and Analysis

2.1. Region Selection

To select βγδ ARs in Cycle 23, we based our study on the following two datacatalogues: USAF-MWL (also known as USAF-SOON) 1 and USAF/NOAAsunspot data 2. The former data base is compilation of daily solar reports of sixground-based observatories. The latter mainly consists of data based on spaceobservations after the launch of the SOHO spacecraft. When the type of an ARis assigned differently in the two catalogues, we choose the more complex one ofthe region as the representative. In this way we selected 200 βγδ regions whichare classified so at least once during their lifetime. Four ARs classified as βγδ inthe catalogues were excluded from our dataset as they showed no sign of δ-typein our visual check with SOHO/MDI images. Finally we found and selected 31candidates which can be studied from their initial emergence on the visible solardisk with reference to the Solar-Monitor website 3.

2.2. Imaging Data

To follow the evolutions of ARs, we used the longitudinal magnetograms andthe continuum images taken with SOHO/MDI with a cadence of 96 min anda pixel size of 2.0′′. We utilized the Geostationary Operational Environmental

Satellite (GOES) X-ray data to estimate the total flare activity of selected ARs.Full-disk Fe xii 195A images of the Extreme ultraviolet Imaging Telescope (EIT;Delaboudiniere et al., 1995) on board SOHO taken with a cadence of 12 min anda pixel size of 2.6′′ were used to check coronal structures. The Transition Region

and Coronal Explorer (TRACE; Handy et al., 1999) images in 195A, 1600A, and5000 A taken with approximately 1 min cadence and 0.5′′ per pixel were alsoused if available.

2.3. Image Analysis

2.3.1. Alignment of AR Images

A time-series of MDI images of a target AR was aligned by the method proposedby Chae (2001) and Chae et al. (2001). We converted original 2 arcsec resolutionimages into 1 arcsec ones, and then applied a non-linear mapping to remove thedifferential rotation effect. With these aligned images, we studied the evolutionof the target AR, and measured the duration of the δ-state by comparing themagnetograms with the continuum images. In this study, we set the brightnesslevels of 0.9 for penumbrae and 0.65 for umbrae relative to the intensity of thequiet region (see Figure 1).

1ftp://ftp.ngdc.noaa.gov/STP/SOLAR DATA/SUNSPOT REGIONS/USAF MWL2http://solarscience.msfc.nasa.gov/greenwch.shtml3http://www.solarmonitor.org/

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Figure 1. A magnetogram (top, gray scale) and a white light image (bottom) of NOAA10314. Green and red contours show the intensity levels of 0.9 and 0.65 of the quiet region(QR) intensity and delineate QR-penumbra boundaries and penumbra-umbra boundaries,respectively (the middle panel). The AR has δ-configuration in the central part.

2.3.2. Circulation

When we closely looked at the evolution of an AR, some sunspots exhibitedprominent rotation around their centers. We estimated the magnitude of rotationby measuring the spatially integrated vorticity around the rotating sunspot inthe following manner. First, we re-aligned the sunspot location in each sequentialmagnetogram to the center of gravity of the magnetic field strength to remove theeffect of proper motion of the sunspot. Second, we applied the local correlationtracking method(LCT; November and Simon, 1988) to these images to derivethe horizontal velocity field (v) around the sunspot. Then, we calculate the areaintegral of the vorticity, namely circulation (C), by

C =

∫(∇× v)zdS, (∇× v)z =

∂vy

∂x−

∂vx

∂y. (1)

We trimmed away the edge zone of three-pixel width from the vorticity fieldto remove fluctuating and erroneous values before the final estimation of thecirculation. The procedure of trimming is done by first making a binary imagefrom the original vorticity map, and then applying the erosion function ERODEin the IDL (Interactive Data Language) software to the binary image whichresults in the shrinkage of island areas in the binary image by three pixels,and finally masking the original vorticity map with the eroded binary image.An example of our method for the vorticity field at 17:35UT on 16 January2005 is shown in Figure 2. From left to right, the velocity field overlaid on themagnetogram, the vorticity field, and trimmed-away map of the vorticity fieldare shown. Erroneous vorticity values originate at the border between the realvelocity field and the quiet region where the velocity of magnetic features is zero.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 2. Erosion operation applied to the vorticity field at 17:35UT on 16 January 2005.From left to right are shown a magnetogram, a vorticity field, and the edge-trimmed mapof the vorticity field, respectively. The velocity field (yellow arrows) and neutral lines (greencontours) are overlaid on the magnetogram (gray scale).

The erosion operation can eliminate the contaminations from the real rotationalelements around the target sunspot effectively as shown in Figure 2.

According to the mathematical definition of circulation, positive (negative)circulation corresponds to counter-clockwise (clockwise) rotation. Note that thesigns are opposite to those of the magnetic twist described in Section 2.3.4.

2.3.3. Tilt Angle of δ-Spots

The temporal variation of the tilt angle (i.e. the inclination angle of the line con-necting the bipoles) tells us the orientation of the kink in an emerging magnetictube. Figure 3 schematically shows the case of a tube with left-handed writhe;upward-kinked (left panel) and downward-kinked (right panel).

When they emerge through the photosphere, the tilt angle rotates in theclockwise (CW) direction in both cases. The distance between the footpointsincreases for the upward-kinked case, while it decreases for the downward-kinkedcase. When the tubes with right-handed writhe emerge, the rotation is in thecounter-clockwise (CCW) direction and the distance between the footpointschanges according to the kink direction as in the left-handed case. Thus wecan infer the orientation of the kink in the emerging magnetic tubes from thetemporal variations of the inclination angle and the distance between the twospots.

2.3.4. Sign of Magnetic Helicity

A “magnetic tongue” pattern is proposed as a useful parameter to give the sign ofmagnetic helicity of the emerging field (Lopez Fuentes et al., 2000; Lopez Fuentes et al.,2008; Luoni et al., 2011). When a twisted tube emerges above the photosphere,the spatial distribution of photospheric magnetic field has an elongated shapelike a tongue. The tongues of different polarities show anti-parallel orientationsalong the neutral line. Since the orientation of a tongue pattern depends on the

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Figure 3. Illustrations of the emergence of tubes with left-handed writhe in the cases ofupward-kinked and downward-kinked configurations. In both cases, the inclination angle ofthe line connecting the two footpoints rotates clockwise and their separation increases ordecreases according to the orientation of the kink.

sense of twist of the emerged tube, we can use this parameter as a proxy ofthe sign of helicity (twist) of the emerging magnetic tube as shown in Figure 4(see also Figure 1 of Luoni et al., 2011). The circulation of a sunspot is anothermeasure of the sign of helicity of the magnetic flux tube, and consistency can bechecked by comparing of these two signs.

To avoid confusion, we here reiterate the definitions for the handedness; thesign of the left (right)-handed twist or writhe is negative (positive).

2.3.5. Flare Index

Several authors have used the soft X-ray flare index (FI) as a proxy of theactivity level of ARs, as given by (e.g. Antalova, 1996; Joshi and Joshi, 2004;Abramenko, 2005; Jing et al., 2006)

FI = 1.0×∑i

mC + 10.0×∑j

mM + 100.0×∑k

mX, (2)

where mC, mM, and mX are the GOES soft X-ray peak intensity magnitudes(from 1.0 to 9.9) of C, M and X-class flares. The indices i, j, and k designateflares in each class per unit time period. For an AR, two kinds of periods wereconsidered in this article; those in which the AR was visible on the disk andthe AR was in the δ-state. We do not consider small flares less than the C-classin this study because they tend to be frequently hidden by major flares or areindistinguishable from the background level.

3. Results

The δ-spots studied in this article can be classified, from the point of view of theemergence morphology, the magnetic connection, the helicity of sunspots, andthe flare activity, into the following groups: i) top-to-top collision, ii) writhedloop, iii) quasi-β, and iv) the others. The majority of δ-spots in our sampleare classified into the first three groups. In the next subsection, we select anddescribe the features of a representative example of each group to show ourclassification scheme.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 4. Sample images of magnetic tongues. When the head parts of the “Yin-Yang”structure forming the magnetic tongues show clockwise or counter-clockwise orientation, theyindicate negative or positive magnetic helicity, respectively.

3.1. Case Studies

3.1.1. Evolution of NOAA10720

NOAA10720 was the most flare-productive region in our samples. It had thelongest δ-duration (longer than 213 h), and showed rapid expansion since itsemergence.

The magnetic and morphological evolution of the region was as follows. First,an emerging flux region (EFR1) emerged as a simple β magnetic configurationwith almost east-west orientation obeying Hale’s law. Then it expanded rapidlyin size and evolved to the δ-configuration on 12 January 2005 as shown inFigure 5. Another new highly sheared EFR (EFR2), which disobeyed Hale’slaw, appeared on the neutral line as if it tried to penetrate into the oppositepolarity portion of EFR1 at around 16:00UT on 13 January 2005.

In Figure 5, we cannot see any signature of writhe in EFR1, as its tilt showedno systematic rotational movements. The magnetic tongues of EFR1 in theinitial emerging phase indicated negative magnetic helicity as shown in the firstrow of Figure 5. This means that the tube emerged with a left-handed twist.Unfortunately, the tongue pattern could not clearly be seen after the vigorousand complex development of EFR1.

On the other hand, the tilt angle of EFR2 showed a slow CW rotation,suggesting the emergence of a loop with left-handed writhe. The twist of themagnetic tubes can be estimated by the circulation around the footpoints of themagnetic tubes, i.e. sunspots.

Now let us see the distribution of vorticity around sunspots of p2 and n2 shownin Figure 6. By specifying the integration area with a circle or an ellipse, whichcovers the target sunspot as compactly as possible, we estimated the circulationover the area covering each sunspot. The reliability of the circulation value wasestimated by changing the size of the calculation area. The area was enlargedor reduced by 2 arcsec for this purpose. Besides the procedures described inSection 2.3.2, we masked the opposite polarity areas before the integration toavoid contamination. The temporal evolution of the circulation of each sunspot

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is displayed in Figure 7. Both sunspots showed generally positive circulationalthough they showed negative values at times. When we closely looked at thevorticity map and the motions of small sunspots in the neighborhood of then2 spot for a day on 16 January, we found that the rapid sliding motions ofsmall sunspots relative to the static environment were recorded as false negativecirculation. If we take this contamination into account, we can assume thatthe circulations around the p2 and n2 spots were mostly positive during theevolution, which means that the footpoints of the magnetic tube of EFR2 showeda CCW rotation during their evolution. Therefore, EFR2 can be considered asan emerging loop of a left-handed twist.

The timing of the flaring in the region is shown in Figure 8. After theemergence of EFR2 on 13 January, many flares have occurred, including threeX-class flares. High activity triggered by the emergence of EFR2 reminds usof the top-to-top collision model proposed by Ikhsanov et al. (2004). The flaremorphology gave us additional information on the magnetic helicity of EFR2.The SOHO/EIT 195 A image in the left panel of Figure 9 shows an inverse-Sshaped structure over EFR2 after the X1.2 flare that peaked at 0:43UT. Theinverse-S sigmoid morphology indicates the left-handed twist of the magnetictube. The TRACE 1600 A image in the right panel of Figure 9 shows bright loopsconnecting the two polarities of EFR2. Guo et al. (2013) argued that negativehelicity was accumulated in EFR2 by a model of non-linear force-free fields,suggesting the emergence of a tube with a left-handed twist.

Thus, we conclude that the significant flare activity of NOAA 10720 is dueto the emergence and the intrusion of the twisted and writhed EFR2 into themagnetic neutral line of the pre-emerged EFR1. This region is a typical exampleof the top-to-top collision formation of an active δ-type spot.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 5. SOHO/MDI magnetograms (left) and white-light images (right) of NOAA 10720corresponding to subsequent days of observations. Identified two EFRs are shown in the fourthrow. The field of view (FOV) of each panel is 300 × 200 arcsec.

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Figure 6. White light images (left), magnetograms (middle), and vorticity fields (right) ofthe positive (top row) and negative (bottom row) polarity areas of EFR2, respectively. Thesize of each FOV is 100 × 100 arcsec, and its center is at the center of gravity of magneticflux distribution. In the middle panels are overlaid the velocity fields (yellow arrows) and theneutral lines (green contours). The areas used to compute the circulation are shown by a circleof 28 arcsec radius in the top row and by an ellipse in the bottom row whose major and minoraxes are 24 and 18 arcsec, respectively.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 7. Time variations of circulation (thin solid lines) and magnetic flux (dashed lines)in sunspots p2 (top) and n2 (bottom) in NOAA 10720. The thick solid line shows the runningaverage of circulation over five consecutive data points in each panel. The error bars indicate apossible range of the circulation values when the size of the analysis area is changes (see text).Vertical lines represent the times of the X-class flares. The magnetic flux values are evaluatedfor the full FOV of Figure 6.

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Figure 8. Time evolution of umbra (dashed), penumbra (dash-dotted), and total sunspot(solid) areas in NOAA 10720. Vertical lines indicate X-class (brown solid), M-class (orangedashed), and C-class (blue dotted) flares, respectively. The horizontal thick green line at thetop represents the duration of the δ-state. The triangle at the bottom indicates the centralmeridian passage of the region.

Figure 9. Left: A SOHO/EIT 195A image (in negative print) of NOAA 10720 taken at01:47 UT, 15 January 2005, after the X1.2 flare peaked at 01:02 UT. White arrows indicatetwo polarities of EFR2. An inverse-S shaped structure is clearly seen. Right: A TRACE 1600Aimage taken at 03:51 UT on 15 January 2005 between the two X-class flares. A bright structureexisted between the two polarities of EFR2 even in a relatively quiet period of flare activity.Overlaid contours (red for positive and blue for negative polarities) show the line-of-sightmagnetic fields of 1500 gauss (G) and 100 G (only in the left panel). The FOV of both imagesis 300 × 300 arcsec.

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Evolution and Flare Activity of δ-Spots in Cycle 23

3.1.2. Evolution of NOAA10826

A day after the emergence of 29 November 2005, NOAA10826 formed a δ-configuration and showed high flare activity in the δ-duration of 56 h.

Its magnetic and morphological evolution is shown in Figure 10. Two EFRsemerged in succession along the east-west line. The δ-configuration was formedbetween the following sunspot of EFR1 and the preceding sunspot of EFR2.

The magnetic tongue patterns of EFR1 and EFR2 showed the sign of negativehelicity (the top row of Figure 10), suggesting the emergence of magnetic tubeswith a left-handed twist. The tilt of the δ-configuration rotated in the CWdirection, with an average rotational speed of 35 day−1, which is similar to thespeed of 30 day−1 measured in NOAA10314 by Poisson et al. (2013). As theseparation between the umbrae of the δ-spot decreased in the first stage, thisδ-configuration behaved as the emergence of a tube with left-handed writhe anddownward kink. As the twist had the same sign as the writhe, we suggest thatthe tube was kinked downward due to transformation into the writhe from thetwist in the layers below the photosphere.

The magnetic twist of EFR1 and EFR2 was studied by the circulation at thefootpoints of EFRs. We have selected sunspots n1 of EFR1 and p2 of EFR2 forthe evaluation of circulation, as they were isolated and free from possible con-tamination. From the temporal variations of the circulation shown in Figure 11,we conclude that the circulations in both sunspots were predominantly positive,which means that the sunspots in the two EFRs rotated in the CCW direction,i.e. the tubes emerged with a left-handed twist.

High flare activity in this region started just after the formation of the δ-configuration, producing 17 flares in total (4 M-class and 13 C-class) during itsdisk passage and 11 flares (3 M-class and 8 C-class) during the δ-configuration(Figure 12). The flare morphology gave some insight on the topology near theneutral line of the δ-configuration. Figure 13 shows the case of an M1.0 flare. Wecan see that the bright flare strand had a highly sheared structure with a left-handed twist. Since the bright strand was probably produced by the magneticreconnection in the corona, we can infer that the magnetic field near the neutralline had left-handed helicity before the flare explosion.

All the direct or indirect evidence indicates that the EFRs in this region hadthe same left-handed helicity. As the magnetic fluxes of sunspots n1 and p2 wereof the same order of magnitude (Figure 11), it is natural to assume that the twoEFRs were not physically separated but connected like a single writhed structureas in the case of NOAA 10314 reported by Poisson et al. (2013). Therefore weclassify this region as the “downward knotted” type.

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Figure 10. SOHO/MDI magnetograms (left) and white-light images (right) of NOAA 10826.Identified two EFRs are shown in the second row. The FOV of each panel is 300 × 200 arcsec.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 11. Time variations of circulation (thin solid lines) and magnetic flux (dashed lines)in sunspots n1 (top) and p2 (bottom) in NOAA 10826. The format is the same as in Figure 7.

Figure 12. Time evolution of umbra (dashed), penumbra (dash-dotted), and total sunspot(solid) areas in NOAA 10826. The format is the same as in Figure 8.

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Figure 13. A high-pass filtered TRACE 195 A image (in negative print) of NOAA 10826.Contours indicate line-of-sight magnetic fields of 500 G (thick) and 100 G (thin) in positive(red) and negative (blue) polarity areas. After the M1.0 flare, highly-sheared bright structuresappeared on the δ-part of the region.

3.1.3. Evolution of AR NOAA10050

NOAA10050 emerged on 26 July 2002. Although the region developed due tosuccessive emergence of several EFRs, the flare activity was not high. A fewδ-configurations formed and disappeared within their lifetime of less than aday at different locations in the region. See Figure 14 for the magnetic andmorphological evolution of the region.

The EFRs in the region emerged with their axes in the east-west direction.As they evolved, the two opposite polarities of each EFR were separated witheach other and sunspots of each polarity merged into a dominant center. Theevolution was very similar to the bipolar emergence model of Zwaan (1978).The δ-configuration formed transiently when a pair of small opposite polarityelements incidentally came together. We found no signature of writhe pattern intheir motion.

The temporal evolutions of circulation around the dominant polarities areshown in Figure 15. The preceding negative polarity changed its circulationfrom negative to positive significantly in the early phase of the evolution. Afterseveral changes in its sign, the positive circulation became dominant in thelater phase. On the other hand, the following positive polarity always indicatednegative circulation during the period. The circulations of the two polarities hada tendency to show opposite directions. Furthermore, the evolution of circulationwas influenced strongly by the successive merging of small sunspots. Therefore,we may conclude that the actual twist of the dominant sunspots was not high.The flare activity in the δ-state of this region was very modest as shown inFigure 16.

The evolution of the region is very similar to the β-type and we classify theregion as the “quasi-β” type.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 14. SOHO/MDI magnetograms (left) and white-light images (right) of NOAA 10050.The FOV of each panel is 350 × 200 arcsec.

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Figure 15. Time variations of circulation (thin solid lines) and magnetic flux (dashed lines)in the preceding negative polality sunspot (top) and the following positive polarity sunspot(bottom) in NOAA 10050. The format is the same as in Figure 11. Dotted vertical linesrepresent C-class flares.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 16. Time evolution of umbra (dashed), penumbra (dash-dotted), and total sunspot(solid) areas in NOAA 10050. The format is the same as in Figure 8.

3.2. Statistical Study

In our case studies of δ-spots, we notice high flare activity in magneticallycomplex δ-spots. In this subsection, we will statistically analyze the dependenceof the flare activity on the characteristic parameters of δ-spot regions.

3.2.1. Parameters

In Table 1, we summarize several flare indices and the parameters which char-acterize the 31 ARs we studied. The peak soft X-ray flux (XRmax) and FI arethe flare indices, while the maximum sunspot area (Smax), the maximum umbralarea (SUmax), δ-term (the duration of the δ-state), the handedness of twist andwrithe, and the type of δ-spot formation are the characteristic parameters ofARs. We will comment on the values of the listed parameters in the followingparagraphs.

An AR develops and changes its magnetic type and sometimes passes throughthe west limb keeping its high activity. To eliminate possible ambiguity anduncertainty in the estimated parameters, we only considered the events thatoccurred in longitudes less than W70. The values of FI were thus countedand listed in Table 1. The values in parentheses are for the flares that occurredduring the δ-state of the region. The identification of the δ-state was also limitedto longitudes less than W70, so that it gives a lower limit in some cases.

The δ-state in an AR was not always continuous in time. If there appearedmultiple δ-states intermittently in an AR, we summed all the time spans of δ-periods to obtain the “δ-duration”(or “δ-term”) in this study. When there wasa gap longer than several hours in the available MDI continuum images, wealso used TRACE white light images to estimate the δ-duration. However, thereremained the uncertainties ranging from seven to 31 hours, which is regarded asestimation errors for the δ-duration.

As seen in our case studies, the magnetic field distributions in βγδ ARs arecomplex and the estimation of the magnetic twist from the circulation is some-times ambiguous. However, it is well known that the preceding sunspots have

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more rigid structure and longer lifetime than the following sunspots (van Driel-Gesztelyi and Petrovay,1990), while the following sunspots tend to be affected by turbulent motions inthe surroundings which cause the fragmentation of the flux tube (Fan et al.,1993). Therefore we mainly measured the circulation of the preceding sunspotsand adopted their handedness of twist as more reliable representatives of theARs. To decide the sign of writhe, we considered the evolution of the δ-part asdescribed in Section 2.3.3.

The flare that corresponded to the peak X-ray flux represents only a singleevent of an AR through the observational period and the event did not alwaysoccur in the δ-state. On the other hand, FI can be measured over the definiteperiod of the δ-duration. Therefore, we regarded FI as a better parameter offlare activity in the δ-state than XRmax.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Table 1. Summary of parameters for 31ARs studied. The upper part of the table isfor ARs in the northern hemisphere, while the lower part is for those in the southernhemisphere. Here, XRmax means the peak X-ray flux in the observed period of eachAR. Flare Index indicates the value integrated over the observed period (the value in-tegrated over the δ-state is shown in parentheses). Smax means the maximum sunspotarea in the observed period. SUmax means the maximum umbral area in the observedperiod (the value in the δ-state is shown in parentheses). δ-term shows the integratedduration of the δ-state. The twist and writhe are indicated by R (right-handed) or L(left-handed) . The “Type” column show the emergence type of ARs; TT (top-to-top),DK (downward knotted), UK (upward knotted), and QB (quasi-β), respectively.

ARXRmax

(Wm−2)Flare Index

Smax

(Mm2)

SUmax

(Mm2)

δ-term(h)

Twist Writhe Type

9165 59.0 257.0 (42.2) 1851 291 (280) 24 L L UK

9511 120.0 275.9 (247.5) 714 114 (114) 20 R R DK

9678 20.0 103.1 (40.3) 3046 623 (584) 26 L toR L DK

9901 40.0 53.1 (53.1) 2003 283 (283) 188 — R —

10412 9.8 22.8 (6.0) 944 170 (160) 27 R R DK

10488 19.0 191.8 (191.8) 6786 1789 (1789) 158 L L DK

10564 110.0 219.0 (209.0) 3716 659 (659) 110 — — TT

10696 250.0 1114.9 (1062.1) 3841 829 (829) 192 L L TT

10720 710.0 2299.3 (2299.3) 6906 2147(2147) 213 L L TT

10956 2.9 3.9 (2.9) 1054 151 (151) 112 — — —

8506 3.3 9.1 (0.0) 1285 245 (211) 8 R — QB

8926 2.3 96.6 (41.6) 805 152 (152) 52 L L DK

9494 10.0 59.9 (26.7) 1105 251 (159) 32 R R DK

9775 22.0 115.3 (11.0) 1415 144 (144) 32 L L DK

9900 4.4 11.2 (0.0) 633 75 (67) 10 — — —

9904 9.2 8.2 (0.0) 247 52 (52) 30 — L —

9906 26.0 58.1 (48.5) 2907 540 (540) 114 R R DK

10017 150.0 282.5 (174.4) 2298 341 (341) 34 R R TT

10050 8.6 57.5 (6.5) 3408 627 (600) 38 — — QB

10119 8.8 54.9 (14.0) 3192 541 (541) 92 L — QB

10137 40.0 174.7 (170.0) 1330 252 (252) 88 L L DK

10226 68.0 231.6 (124.0) 2812 578 (578) 110 L R DK

10314 150.0 511.1 (443.9) 2367 635 (635) 94 R toL R DK

10417 5.2 39.7 (6.9) 1405 199 (158) 15 — — QB

10456 4.4 6.6 (2.2) 772 101 (60) 14 — — QB

10551 3.2 6.9 (0.0) 1531 221 (221) 38 — — QB

10591 12.0 12.0 (12.0) 412 82 (82) 32 R — —

10798 56.0 84.8 (84.3) 2931 461 (461) 65 R — TT

10826 78.0 204.7 (200.9) 2152 390 (390) 56 L L DK

10848 41.0 14.9 (0.0) 1466 181 (181) 21 — — —

10865 14.0 30.0 (0.0) 2532 568 (285) 38 — — QB

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Figure 17. Smax (left) and FI (right) versus the penumbral-umbral radius ratio in the δ-state.

3.2.2. Flare Activity and Sunspot Area

Sammis et al. (2000) statistically studied the relation between the flare activityand the maximum sunspot area for the ARs in Cycle 22, and found that ARswith larger maximum sunspot area produced higher peak X-ray flux. Especiallythey showed that βγδ-ARs had the largest maximum sunspot area and henceproduced the strongest flares. Now we will check the relation between the FI(the proxy of flare activity level) and the maximum umbral area for our sampledβγδ-ARs in Cycle 23.

First, we confirm that the relation found by Sammis et al. (2000) also holdsin our data. The physical meaning of the relation is that the sunspot area isa measure of the total magnetic flux of the region and hence represents themagnetic energy content of the region. The ARs with large content of magneticenergy can produce large release of energy as flaring. As we do not have themagnetic flux values for all the ARs in Cycle 23, we have to use the measuredarea as a proxy parameter for the magnetic flux. The line-of-sight magnetic databy SOHO, for example, cannot provide a reliable estimate of the magnetic flux,without the correction for the projection effect and the field inclination to thevertical. We took the umbral area as a better proxy parameter of the magneticflux than the total sunspot area including the penumbral area, because of tworeasons. The first is that larger sunspots have smaller contribution of penumbrato the total sunspot area (left panel of Figure 17) and contain more magneticflux in the umbral area (Antalova, 1991; Jin et al., 2006). The other empiricalreason is that FI does not depend so strongly on the penumbra-umbra radiusratio when this ratio is high (right panel of Figure 17).

Next, we notice large dispersion in FI in Figure 18. For a given maximumumbral area, there appears a variety of ARs from highly flare productive onesto less productive ones. In Figure 18, βγδ ARs are roughly split into differentemergence types, suggesting that the emergence mode is another key parameterto characterize the flare productivity. By comparing the two panels in the figure,

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 18. Flare index versus maximum umbral area in a logarithmic scale. The left panelis for the data in the observed period and the right panel is for those in the δ-state. SixARs which showed no flare activity in the δ-state were excluded. Different symbols indicate“top-to-top” (red circles), “writhed” (orange squares, both DK and UK types in Table 1),“quasi-β” (blue triangles), and “others” (gray diamonds), respectively. The error-bars wereassigned by considering the effect of data gaps (see text). The results of non-linear least-squaresfitting (power-law index kNL) and classical least-squares fitting (power-law index kC) are shownby the solid and the dashed lines, respectively.

we can see that the separation of the three groups in the right panel is clearerthan in the left panel. Since the clear separation into groups may give hints of theδ-state, we will mainly concentrate to the flare activity and the area variationin the δ-state hereafter.

3.2.3. Flare Activity and Emergence Type

Figure 19 shows the histogram of SUmax and FI distributions grouped accordingto the emergence type in the δ-state. We combined the groups DK (downward-kinked) and UK (upward-kinked) in Table 1 as the “writhed” type. The binsizes of SUmax and FI are 100.4(≈ 2.51) and 100.7(≈ 5.01), respectively. Thegrouping follows the decreasing order of magnetic complexity (i.e. “top-to-top”,“writhed”, “quasi-β” and “others”). As the topological complexity decreases,both SUmax and FI distribute to lower values. The relation found here clearlyindicates that the flare activity of βγδ ARs depends not only on the umbral areabut also on the magnetic complexity. Moreover, it suggests that the large totalcontent of magnetic flux represented by the umbral area is a necessary conditionand significant magnetic complexity may be another more stringent necessarycondition for the activation of strong flares.

3.2.4. Twist and Writhe of δ-Spots

When we classified the 31 ARs by their emergence mode, we found 5 ARs as“top-to-top”, 13 as “writhed”, 7 as “quasi-β” and 6 as “others”. Although the

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“quasi-β” and “others” groups hardly ever showed the signs of twist and writhe,the “top-to-top” and “writhed” ARs clearly showed the twist and writhe. Inmost cases of the “writhed” type, the signs of twist and writhe agree with eachother at least in their initial phase (12 cases out of 13). This result stronglysuggests that the formation of the δ-spot is not due to the gathering of disjointedEFRs but due to the emergence of a singly connected structure (left panel inFigure 20). The“top-to-top” ARs also show high probability of agreement intheir helicity signs (three cases out of five). We speculate that the “top-to-top”type has a more developed writhing structure than the “writhed” type (rightpanel of Figure 20). However, according to the study of Park et al. (2012), some“top-to-top” ARs may be associated with the injection of opposite-sign helicitiesthrough flux emergence. Therefore the model of “top-to-top” ARs is at presentcontroversial and further investigation is necessary to finalize the model.

The majority of “writhed” ARs were of DK type (12 cases out of 13). TheUK type was quite rare. The dominance of DK seems natural because a simplewrithed magnetic tube with upward kink will emerge through the photosphereas a normal β-type magnetic distribution and will rarely be identified as theδ-type sunspots.

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Evolution and Flare Activity of δ-Spots in Cycle 23

Figure 19. Histograms of umbral area maximum (left) and FI (right) in the δ-state period.From the second row downward are shown “top-to-top”, “writhed”, “quasi-β”, and “others”types, respectively, and the top row shows the total.

3.2.5. δ-Duration and Emergence Type

As shown in the left panel of Figure 21, more magnetically complex ARs havelonger δ-duration. We already confirmed that more magnetically complex ARshave larger maximum umbral area in Figure 18.

In general, larger sunspots have longer lifetime (Gnevyshev, 1938; Waldmeier,1955). Recurrent sunspot groups are found to exhibit a slightly larger lifetimethan that based on the Gnevyshev-Waldmeier relationship by Petrovay and van Driel-Gesztelyi(1997). It is also well known that larger sunspots tend to be darker and havestronger magnetic fields (Solanki, 2002; Livingston, 2002). Furthermore, Shi and Wang(1994) reported that the productivity of δ-spots for X-class flares is closelycorrelated to the lifetime of δ-spots. Our result suggests that the long lifetime of

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Figure 20. Schematic models for βγδ ARs. The left panel shows a general model for thedownward-knotted type such as NOAA 10826. The right panel shows a possible model for the“top-to-top” type such as NOAA 10720.

active δ-spots is closely related to their magnetic complexity (twist and writhe).Although magnetic tubes are eventually dispersed due to the action of turbu-lent convection (Petrovay and Moreno-Insertis, 1997) and/or fragmentation byfluting instabilities, the twisted tubes are more resistant against these dissolvingactions. It seems difficult that the magnetic lines of force of the tube above thesolar surface will be torn off by convective motions in lower layers, as the linesof force are entangled and hooked to the magnetic tube in the corona. Further,the twist will suppress the fluting instability of magnetic tubes (Priest, 2014).Threfore, we argue that the longevity of an active δ-spot depends on its magnetictwist.

3.2.6. Possible Power-law Relations among Parameters

On every scatter plot (Figures 18 and 21), we performed the power law fittingto the data. Two methods were used to derive the power-law index k. The firstis the classical least-squares fitting (C-LS) to log-log plots and we obtain thepower-law index kC. The second is the non-linear least-squares fitting (NL-LS)method based on the Gauss-Newton algorithm (cf. Hansen et al., 2012), leadingto kNL. For the data points in the left panel of Figure 18 (SUmax vs. FI in theobserved period), we found kC = 1.21± 0.24 and kNL = 1.61± 0.33. In the rightpanel of Figure 18 (SUmax vs. FI in the δ-state), we found kC = 1.30 ± 0.31and kNL = 1.87 ± 0.50. FI follows a power-law dependence on SUmax with anindex around 2, especially in the δ-state. It is worthwhile to note that Magara(2014) discussed a power-law relationship between the magnetic free energy andthe total magnetic flux for twisted emerging loops with an index of 2 from hisnumerical simulation.

We next show the relation between the δ-duration and FI in the δ-state (leftpanel of Figure 21). Although we could not get the converged solution of NL-LS,we obtained kC = 1.54±0.34 when we excluded the “others” group as they havelarge dispersion. For the relation between the δ-duration and SUmax in the δ-state (right panel of Figure 21), we found kC = 0.76±0.16 and kNL = 1.07±0.28.Combining the last two relations, namely both plots of Figure 21, we can infera power-law relation FI ∼ S 2.0

Umaxfrom C-LS which is consistent with the result

derived in the previous paragraph.

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Evolution and Flare Activity of δ-Spots in Cycle 23

.

Figure 21. Flare Index (left) and maximum umbral area (right) in the δ-state as a functionof the δ-duration. The symbols are the same as in Figure 18. Six ARs which showed no flareactivity in the δ-state were excluded. The error-bars were assigned by considering the effectof data gaps (see text). The results of non-linear least-squares fitting (power-law index kNL)and classical least-squares fitting (power-law index kC) are shown by the solid and the dashedlines, respectively.

4. Discussion

By paying attention to the initial phase of βγδ ARs in Cycle 23, we investigatedwhat are the important configurations which lead to the flare activity. From ourinvestigation, we discovered three representative topological types which havestrong correlations with the flare activity, namely “quasi-β”,“writhed”, and “top-to-top”. We confirmed that the ARs with higher topological complexity showstronger flare activity.

It is interesting to note that almost all ARs classified as the “writhed” typeare of DK type. Once the downward knot structure is formed, a dense plasma“reservoir” is formed in the knot and the whole structure of the flux tubemay become stable owing to the effect of the mass as an anchor (left panel ofFigure 20). Under a different situation, Magara and Longcope (2003) proposed asimilar idea in their numerical simulation of the emergence of a twisted flux tubein the convection zone. Subsequently, Magara (2011) has studied the case of theemergence of a U-loop formed below the photosphere. van Driel-Gesztelyi et al.(2000) have reported that the emergence of a U-loop which connected the oppo-site polarity legs of two Ω-loops below the photosphere. Recently, Poisson et al.

(2013) studied the possibility of a downward kinked structure in the mid part ofNOAA10314. Thus the idea of DK structure is not so exceptional and applicableto twisted magnetic tubes, with several evidence. The DK structure as an anchormay contribute to the stability of the AR.

Subsequently we checked the case of the “top-to-top” group. They show cleartwist and writhe structures with common handedness (three cases out of five).

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Therefore, we infer that the three-dimensional collision is not an accidental onebut is attributed to the extreme development of a writhing structure. For exam-ple NOAA10696, classified as the “top-to-top” type, had the second strongest FIin our sampled ARs and showed both characters of three-dimensional collisionand downward knotted structure. The AR is namely a hybrid type of “writhed”and “top-to-top”. Such a configuration of this AR reminds us that there may becontinuity of developments between the “top-to-top” and “writhed” structures.We propose a schematic model for NOAA10720 with a highly writhed structureas shown in Figure 20 (right panel). We can point out that a similar, highlywrithed model for NOAA 7926 was proposed by Pevtsov et al. (1998).

Brown et al. (2003) studied the rotation of seven sunspots using high resolu-tion white light images with TRACE. They proposed that a possible mechanismfor sunspot rotation is the emergence of a pre-twisted flux tube. On the otherhand, Yan et al. (2009) claimed that the rotation of sunspots originates from thephotospheric flows, based on their study of combined photospheric and coronalobservations. In our study, the rotation of sunspots themselves and the tiltangle rotation of EFR are rarely observed in small and flare-inactive ARs. Ifthe rotation is mainly attributed to photospheric flows, rotational motions ofsunspots will be observed commonly regardless of the sunspot size. However, asshown in our statistical study, the ARs of prominent twist and writhe had largerarea and showed stronger flare activity among the sampled ARs. In addition, asdescribed in Section 3.2.5, the pre-twisted flux tube model is in harmony withseveral features of δ-spots. Therefore we conclude that the origin of sunspotrotation is the emergence of the pre-twisted flux tube.

It is known that twist and writhe helicities transform each other in an idealthin flux tube (Calugareanu, 1959; Moffat and Ricca, 1992; Ricca, 1995; Torok et al.,2010). In this study, we adopted a picture in that the initial twist of ARs willbe mostly generated by turbulent flows in the convection zone. When the twistincreases in an AR, the twist transforms into the writhe in the middle part ofthe flux tube by the kink instability (Torok et al., 2010). Then it is natural tofind the sign relationship as seen in this study. The previous studies have shownthat the kink instability facilitates the formation of δ-spots (e.g. Linton et al.,1999). Tian et al. (2005) pointed out that the signs of twist and writhe tend toagree in well-developed ARs under kink instability.

Regarding the classification of δ-spots, we review the relations between thetypes classified by our study and the types by Zirin and Liggett (1987) as in-troduced in Section 1. We can consider that the first type of Zirin and Liggett(ZL) is the same as the “top-to-top” type of ours. The third type of ZL may beequal to the “writhed” group, although we believe that the configuration is notformed by different dipoles but by a connected structure below the photosphere.However, the second type of ZL was seldom observed in our study. This typewas seen in only one or two cases in the “others” group of our study. This typemay be more likely to occur in recurrent sunspots rather than in sunspots intheir young stage studied here. The “quasi-β” type was not considered in theZL classification as they may not produce notable flares.

We discussed the possible power-law relations among the βγδ-spot parame-ters. Our physical interpretation is as follows. FI is a good proxy of the total

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Evolution and Flare Activity of δ-Spots in Cycle 23

energy released in flares in an AR and thus is a measure of the total magneticfree energy of the region supplied by the gas flow field. The maximum umbralarea SUmax is a measure of the magnetic flux of the region. The functionalrelation of a power law sometimes is interpreted as the evidence of a scale-freeprocess (Shimizu, 1995; Shimojo and Shibata, 1999; Nishizuka et al., 2009). Inour case, the total free energy supply or injection can be considered as dueto a kind of scale-free processes, probably the helicity injection process by theturbulent convective flows or the differential rotation. The process seems to workindependent of the total amount of magnetic flux. The difference in FI amongthe emergence-type groups may be the difference in topology of the magnetictubes. While the “quasi-β” type may have a simple form with less twist andless free-energy, the “writhed” type may have a singly knotted or kinked tubewith more free-energy, and the “top-to-top” type may have a doubly or multiplyknotted tube with much more free-energy.

5. Conclusions

We have studied the initial evolution of 31 βγδ ARs and derived the followingconclusions.i) From the point of view of topology, emerging βγδ ARs can be classified broadlyinto three categories: “quasi-β”, “writhed”, and “top-to-top”. The “top-to-top”type has the most complex topology and the “quasi-β” type is the simplest type.The “Writhed” group has medium complexity among the three types.ii) ARs of more complex topology tend to exhibit higher flare activity.iii) The signs of twist and writhe both tend to be consistent with each other inthe “writhed” type.iv) The downward-knotted structure in the mid portion of the flux tube is theessential element of active βγδ ARs.v) The flare activity of βγδ ARs are highly correlated not only with the sunspotareas but also with the magnetic complexity.vi) There is a possible scaling-law between FI and SUmax.

Finally, we will give some comments on the future extension of our study.Direct measurements of magnetic helicity will be essential to study the free-energy accumulation in ARs. Observations of the ARs throughout their lifetimealong with stereoscopic views from space will be desirable. Further it will be animportant challenge to diagnose the magnetic topology of ARs in the convectionzone by improving local helioseismology.

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Takizawa and Kitai

Acknowledgements The authors appreciate useful comments from an anonymous referee.

We thank the SOHO, TRACE, and GOES consortia for their data. SOHO is a international

cooperation between ESA and NASA. We are grateful to the staff of Kwasan and Hida obser-

vatories of Kyoto University, for their continuing help. We wish to thank Hiroki Kurokawa and

Yin Zhang for useful discussion. This work was supported by the Grant-in-Aid for the Global

COE Program “The Next Generation of Physics, Spun from Universality and Emergence” from

the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We are

partially supported by the grant-in-aid from the Japanese MEXT (PI: R.Kitai No.26400235).

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